2 3. Show that that the vector u =|-5 is a linear combination of the vectors vi = -4 and vz = 3.

Q: 8. If {V1, V2,..., ,}is a linearly dependent set of vectors, prove that one of these vectors is a…

A:

Q: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

A: follow next step

Q: 46 4 and j -3 Express the vector v as a linear combination of a -12 y. ||

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Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

A: Linearly independent

Q: 4. Find the vector v that is orthogonal tou=i+j+k and whose r-component and z-component are 2 and…

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Q: EX/ Find The normal vector to A = 2i-3j+4K, B =i-2j+ 5K %3D ĀxB =Ñ =1? ĀXB=N -3 4 = -7i-6j-K %3D - 2…

A:

Q: Let x,y,z be (non-zero) vectors and suppose that z=4x−4y and w=12x−12y−4z. Are the following…

A: A vector is a span of vectors when the first one can be written as the linear combination of the…

Q: as a linear combination of x = 7 4 and y = -3 Express the vector u -2

A: NOTE: Refresh your page if you can't see any equations. . write both vectors x and y in the matrix…

Q: Find the initial point A of the vector that is equivalent to (3,7), and whose terminal point is…

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Q: 18 as a linear combination of a and y Express the vector v y.

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Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

A:

Q: 2 1 3. Show that that the vector u = |-5| is a linear combination of the vectors v1 = |-3 3 2 2 V2 :…

A: The given vectors are: u=2-53, v1=1-32, v2=2-4-1  and  v3=1-57 Vector u=2-53 is a linear combination…

Q: 11. If ā.b = 0, why can we not necessarily conclude that the given vectors are perpendicular? (In…

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Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

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Q: -36 4 3 Express the vector v = as a linear combination of x ar -34 x+ y. %3D ||

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Q: If y is orthogonal to the vectors u and v, then y is orthogonal to u+ 3v. True False

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Q: Г 13 and vz = 14 are linearly independent. Determine whether the vectors v 14

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Q: -11 and ỹ = Express the vector u as a linear combination of x 28 x+ y.

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Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Let x3 = x1 + x2. Determine the length of…

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Q: linear algebra question:

A: The orthogonal projection is given by,

Q: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

Q: If u = x2 + 2x -y and v = - 2xy- 2y, then the vorticity vector is - 3yk 10 -yk 110 YK III

A: We have to solve given problem: Concept:

Q: - a) Determine the vector equation of the line of intersection of these 2 (1) x + 2y + 2z = -3 (2 2x…

A: Note:  part(b) is the independent subpart of part(a) and also it is incomplete. so part (b) can't be…

Q: 8. ... The value(s) of h which makes the vectors linearly dependent is(are) because this will cause…

A:

Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: () () 1. 2.

A:

Q: - 3 7 1 h of h which makes the vectors linearly depe ma to separate answers as needed.)

A:

Q: 18 as a linear combination of = 8 Express the vector i and j =

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Q: Find two linearly independent vectors perpendicular to the w 41 -6- 1

A: Given: vector is v→=4-91 we have to find the two linear independent vectors perpendicular the given…

Q: Which of the following vectors are linearly independent? (2) (0) 21

A:

Q: Suppose a and b are vectors such that axb=(1,

A: Given, a→ and b→ are vectors such that a→× b→=(1, 0, 2).

Q: For what value or values of the constant u are the following vectors are linearly related and are…

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Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

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Q: 3 The vectors u = -4 and v = -12 are linearly independent. 6.

A: Given vectors : u=3-42 and v=9-126 . Therefore,  we will test these two vectors to find whether 'a'…

Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

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Q: Find basis for the set of vectors in R2 on the line y= nx . where n=9.

A: Explanation of the solution is given below...

Q: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

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Q: Is the set of the three vectors S linearly independent? Explain why. S = 2

A: From the definition, a set S=v1,v2,v3 is said to be linearly independent if the linear combination…

Q: Consider the lines L1 and L2 in R³ given by the vector equations L1 :ở = (2,4, 4) + t(4, 1, 5) and…

A: Given: L1 : v→ =2 , 4, 4+t 4, 1, 5 And  L2 : v→ =1, -3, 2+t -2, 3, 1

Q: For what value(s) of a are the following vectors linearly independent: (1,5,-2), (0,6,a) and…

A: The vectors are linearly independent if the matrix formed from these vectors has non zero…

Q: 2 3. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = -3 and v = .3 4

A: What is the inner product of the vector space of 2 by 2 matrices. We assume it is Frobbenius inner…

Q: (1) We have the following 4 vectors v1, v2, v3 and v4. Prove that the vectors are linearly…

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Q: 3. Show that that the vector u = |-5 is a linear combination of the vectors vị = |-3 3 2 V2 = -4 and…

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Q: There are 6 linearly independent vectors in R°. O True False

A: We know that the dimension of the vector space R5 is 5.

Q: Determine if the vector x̄=(-12i-j-5k) can be expressed as a linear combination of ū=(1,-1,0),…

A: The solution of the problem is given in the next steps.

Q: Suppose that u = – 2i – 5j and v = - 3i – Compute the given linear combination of these two vectors.…

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Q: 5. Show that if vị and vz are linearly independent vectors in R?, then any vector w E R² can be…

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Q: 4. For which value of k the vector u = -2 is a linear combination of the vectors 3 3 V1 = 0 and vz =…

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